full width at half maximum

Full width at half maximum (FWHM) is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value.

FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of spectrometers.

The term full duration at half maximum (FDHM) is preferred[who?] when the independent variable is time.

The convention of "width" meaning "half maximum" is also widely used in signal processing to define bandwidth as "width of frequency range where less than half the signal's power is attenuated", i.e., the power is at least half the maximum. In signal processing terms, this is at most −3 dB of attenuation.

If the considered function is the normal distribution of the form

Failed to parse (Missing texvc executable; please see math/README to configure.): f(x) = \frac{1}{\sigma \sqrt{2 \pi} } \exp \left[ -\frac{(x-x_0)^2}{2 \sigma^2} \right]


where Failed to parse (Missing texvc executable; please see math/README to configure.): \sigma

is the standard deviation and Failed to parse (Missing texvc executable; please see math/README to configure.): x_0
can be any value (the width of the function does not depend on translation), then the relationship between FWHM and the standard deviation is[1]
Failed to parse (Missing texvc executable; please see math/README to configure.): \mathrm{FWHM} = 2\sqrt{2 \ln 2 } \; \sigma \approx 2.3548200 \; \sigma.


Another important distribution function, related to solitons in optics, is the hyperbolic secant:

Failed to parse (Missing texvc executable; please see math/README to configure.): f(x)=\operatorname{sech} \left( \frac{x}{X} \right).


Any translating element was omitted, since it does not affect the FWHM. For this impulse we have:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathrm{FWHM} = 2 \; \operatorname{arsech} \left( \frac{1}{2} \right) X = 2 \ln (2 + \sqrt{3}) \; X \approx 2.634 \; X


where arsech is the inverse hyperbolic secant.

References [link]

  1. ^ https://mathworld.wolfram.com/GaussianFunction.html

See also [link]


Stub icon This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.

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Once In A While (ft. Joe Budden)

by: Fame

I can see it
It's funny man
Cause it's like it's not going nowhere
And you gon' see it wherever there's struggle
[Once in a while I do look at you]
I see my pain in your eyes man
[To see that twinkle in your eyes]
So I know you're feelin' me
It's that twinkle man
That sign of struggle
I've seen it
In me
Cause everyday I can't help but see it
People ain't satisfied
And you're hatin' your 9 to 5
and Everybody wanna live another life
But ain't no length you go or mountain you climb
Not to better your days
All That would do is leave room for people to say
"I guess you're livin' better now
Share a little bit of that cheddar now"
Cause I remember days back when
A brother was hustlin' and robbin' too
I done tossed the baretta now
On a whole nother level now
Still I can't enjoy my fame
Unless my people doin' the same
And gettin' money too
[Once in awhile I couldn't look at you]
Oh once in awhile
[and see the twinkle in your eyes]
And I can see that you don't ever wanna struggle no more
[Once in awhile I couldn't look at you]
Once in awhile
[and see the twinkle in your eyes]
And I can see that you don't ever wanna cry no more
Cause every time you ask me, I'm grindin'
It shouldn't have to be that way
You shouldn't have to pay my way
I shouldn't have to want for a brighter day
Got a little little problem on the way
Bounty hunters checkin' state to state
Child support lady on your case
Not to mention tickets you ain't never paid
Oh what must I do
that's what you'll be askin'
God please hold it down for me
Don't let Satan get the hold of me
I'm tryin' to tell you it can happen to me too
But it happened a lot worse to my brother
Muhammad thank God he recovered
[Once in awhile I choose look at you]
Once in awhile
[and see the twinkle in your eyes]
And I can see that you never wanna struggle no more
[Once in awhile I choose look at you]
Look in your eyes
[and see the twinkle in your eyes]
And I can see that you don't ever wanna cry no more
[Once in awhile I choose look at you]
'Cause I see your pain now
'Cause I see your pain now
I can feel you strain now
And I can see you cryin'
And inside you're dyin'
We're no longer the same now
But you got to make change now
[Once in awhile I do look at you]
Once in awhile
[and see the twinkle in your eyes]
And I can see that you don't ever struggle no more
[Once in awhile I do look at you]
Once in awhile
[and see the twinkle in your eyes]
And I can see that you don't ever wanna cry no more
Don't wanna cry no more
And I can see
That you don't ever want to struggle no more




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